Markus Guhe

A formal cognitive model of mathematical metaphors

Starting from the observation by Lakoff and Nunez (2000) that the process for mathematical discoveries is essentially one of creating metaphors, we show how Information Flow theory (Barwise & Seligman, 1997) can be used to formalise the basic metaphors for arithmetic that ground the basic concepts in the human embodied nature.

The roles of haptic-ostensive referring expressions in cooperative, task-based human-robot dialogue

Generating referring expressions is a task that has received a great deal of attention in the natural-language generation community, with an increasing amount of recent effort targeted at the generation of multimodal referring expressions. However, most implemented systems tend to assume very little shared knowledge between the speaker and the hearer, and therefore must generate fully-elaborated linguistic references. Some systems do include a representation of the physical context or the dialogue context; however, other sources of contextual information are not normally used. Also, the generated references normally consist only of language and, possibly, deictic pointing gestures. When referring to objects in the context of a task-based interaction involving jointly manipulating objects, a much richer notion of context is available, which permits a wider range of referring options. In particular, when conversational partners cooperate on a mutual task in a shared environment, objects can be made accessible simply by manipulating them as part of the task. We demonstrate that such expressions are common in a corpus of human-human dialogues based on constructing virtual objects, and then describe how this type of reference can be incorporated into the output of a humanoid robot that engages in similar joint construction dialogues with a human partner.

A computational account of conceptual blending in basic mathematics

We present an account of a process by which different conceptualisations of number can be blended together to form new conceptualisations via recognition of common features, and judicious combination of their distinctive features. The accounts of number are based on Lakoff and Nunezs cognitively-based grounding metaphors for arithmetic. The approach incorporates elements of analogical inference into a generalised framework of conceptual blending, using some ideas from the work of Goguen. The ideas are worked out using Heuristic-Driven Theory Projection (HDTP, a method based on higher-order anti-unification). HDTP provides generalisations between domains, giving a crucial step in the process of finding commonalities between theories. In addition to generalisations, HDTP can also transfer concepts from one domain to another, allowing the construction of new conceptual blends. Alongside the methods by which conceptual blends may be constructed, we provide heuristics to guide this process.

Algorithmic Aspects of Theory Blending

In Cognitive Science, conceptual blending has been proposed as an important cognitive mechanism that facilitates the creation of new concepts and ideas by constrained combination of available knowledge. It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories. This paper describes a logic-based framework which allows a formal treatment of theory blending, discusses algorithmic aspects of blending within the framework, and provides an illustrating worked out example from mathematics.

Game strategies for The Settlers of Catan

We present an empirical framework for testing game strategies in The Settlers of Catan, a complex win-lose game that lacks any analytic solution. This framework provides the means to change different components of an autonomous agents strategy, and to test them in suitably controlled ways via performance metrics in game simulations and via comparisons of the agents behaviours with those exhibited in a corpus of humans playing the game. We provide changes to the game strategy that not only improve the agents strength, but corpus analysis shows that they also bring the agent closer to a model of human players.

Utility‐Based Generation of Referring Expressions

This paper presents two cognitive models that simulate the production of referring expressions in the iMAP task-a task-oriented dialog. One general model is based on Dale and Reiters (1995)incremental algorithm, and the other is a simple template model that has a higher correlation with the data but is specifically geared toward the properties of the iMAP task. The property of the iMAP task environment that is modeled here is that the color feature is unreliable for identifying referents while other features are reliable. The low computational cost of the incremental algorithm for generating referring expressions makes it an interesting starting point for a cognitive model. However, its explanatory power is limited, because it generates uniquely distinguishing referring expressions and because it considers features for inclusion in the referring expression in a fixed order. The first model extends the original incremental algorithm by an ability to adapt to feedback of whether a referring expression was used successfully, but it seems to overpredict the frequency with which distinguishing expressions are made and underpredict the frequency of overspecified referring expressions. The second model produces features for referring expressions purely based on its current estimate of a features utility. Both models predict the observed human behavior of decreasing use of color terms and increasing use of useful feature terms.

Referring in dialogue: alignment or construction?

Human speakers generally find it easy to refer to entities in such a way that their hearers can determine who or what is being talked about. In an attempt to model this behaviour, researchers in computational linguistics have explored the development of algorithms that operate in a deliberate manner, choosing attributes of an intended referent on the basis of their ability to distinguish that entity from its distractors. Psycholinguistic models, on the other hand, suggest that speakers align their referring expressions at several linguistic levels with those used previously in the discourse. This implies more subconscious reuse, and less deliberate choice, than is found in computational models of referring expression generation. Which of these is a more accurate characterisation of what people do? Do both models capture aspects of human referring behaviour? In this paper, we use a machine-learning approach to explore these questions. In our first study, we examine how underlying factors of the psycholinguistic and the computational models impact on the production of reference in dialogue. In our second study, we explore the psychological validity of another crucial aspect of some computational approaches to reference production: their serial dependency characteristic, whereby attributes are included in a referring expression based on which other attributes have already been chosen. The results of both studies suggest that the assumptions underpinning computational algorithms do not play a large role in peoples referring behaviour.

Using Analogical Representations for Mathematical Concept Formation

We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate mathematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of “visual” concepts and conjectures, and present an automated case study in which we enable an automated theory formation program to read this type of visual, analogical representation.

Abstract or not abstract? Well, it depends …

The target article by Cohen Kadosh & Walsh (CK&W) raises questions as to the precise nature of the notion of abstractness that is intended. We note that there are various uses of the term, and also more generally in mathematics, and suggest that abstractness is not an all-or-nothing property as the authors suggest. An alternative possibility raised by the analysis of numerical representation into automatic and intentional codes is suggested.

Persuasion with Limited Sight

Humans face many game problems that are too large for the whole game tree to be used in their deliberations about action, and very little is understood about how they cope in such scenarios. However, when a human player’s chosen strategy is conditioned on her limited perspective of how the game might progress (Degremont et al. 2016), then it should be possible to manipulate her into changing her planned move by mentioning a possible outcome of an alternative move. This paper demonstrates that human players can be manipulated this way: in the game The Settlers of Catan, where negotiation is only a small part of what one must do to win the game thereby generating uncertainty about which outcomes to the negotiation are good and which are bad, the likelihood that a player accepts a trade offer that deviates from their declared preferred strategy is higher if it is accompanied by a description of what that trade offer can lead to.